Ethics Part 1 Concerning God
Propositions 12-20

E1:
PROP. 12. No attribute
of substance
can be conceived from which it
would follow that substance can be divided.

Proof.--The parts into which
substance as thus conceived would be
divided, either will retain the nature of substance, or they will not. If
the former, then (by E1P8) each part will
necessarily be
infinite, and
(by E1P6) self-caused, and
(by E1P5) will perforce consist of a
different attribute,
so that, in that case, several substances could be
formed out of one substance,
which (by E1P6)
is absurd. Moreover, the
parts (by E1P2) would have nothing in common
with their whole, and the
whole (by E1D4 and E1P10)
could both exist and be conceived without
its parts, which everyone will admit to be absurd.
If we adopt the second
alternative namely, that the parts will not retain the nature of
substance
then, if the whole substance were divided into equal parts, it would lose
the nature of substance, and would cease to exist, which
(by E1P7) is absurd.

Proof.--If it could be divided,
the parts into which it was divided
would either retain the nature of absolutely
infinitesubstance, or they
would not. If the former, we should have several substances of the same
nature, which (by E1P5) is absurd. If the latter,
then (by E1P7)
[E1P12]
substance absolutely
infinite
could cease to exist, which (by E1P11) is
also absurd.

E1: PROP. 13, Corollary, Note.
--The indivisibility of substance
may be more easily understood as
follows. The nature of substance can only be conceived as
infinite, and by
a part of substance,
nothing else can be understood than
finite substance,
which (by E1P8) involves a manifest contradiction.

Proof.--As God is a being
absolutely infinite,
of whom no attribute
that expresses the essence of
substance can be denied (by
E1D6), and
he necessarily exists (by E1P11); if any
substance besides God were
granted, it would have to be explained by some
attribute of God, and thus
two substances with the same attribute would exist, which
(by E1P5) is
absurd; therefore, besides God no
substance can be granted, or,
consequently, be conceived. If it could be conceived, it would necessarily
have to be conceived as existent; but this (by the first part of this
proof) is absurd. Therefore, besides God no
substance can be granted or
conceived. Q.E.D.

E1:
PROP. 14, Corollary 1.--Clearly, therefore: 1. God is one, that
is (by E1D6)
only one substance
can be granted in the universe, and that substance is
absolutely infinite,
as we have already indicated (in the note to
E1P10N).

E1:
PROP. 15. Whatsoever is, is in God, and without God nothing can be, or
be conceived.

Proof.--Besides God, no
substance
is granted or can be conceived (by
E1P14), that is (by E1D3)
nothing which is in itself and is
conceived through itself. But
modes
(by E1D5)
can neither be, nor be
conceived without substance;
wherefore they can only be in the divine
nature, and can only through it be conceived. But
substances and
modes
form the sum total of existence (by E1A1),
therefore, without God nothing can be, or be conceived. Q.E.D.

E1: PROP. 15, Note.
--[A.] Some assert that God, like a man,
consists of body and mind, and is
susceptible of passions.
How far such persons have strayed from the truth
is sufficiently evident from what has been said. But these I pass over.
For all who have in anywise reflected on the divine nature deny that God
has a body. Of this they find excellent proof in the fact that we
understand by body a definite quantity, so long, so broad, so deep,
bounded by a certain shape, and it is the height of absurdity to predicate
such a thing of God, a being absolutely
infinite.
But meanwhile by the
other reasons with which they try to prove their point, they show that
they think corporeal or extended substance wholly apart from the divine
nature, and say it was created by God. Wherefrom the divine nature can
have been created, they are wholly ignorant; thus they clearly show, that
they do not know the meaning of their own
words.
I myself have proved
sufficiently clearly, at any rate in my own judgment
(E1P6C, and
E1P8N2), that no
substance can be produced or created by anything other
than itself. Further, I showed (in E1P14),
that besides God no substance
can be granted or conceived. Hence we drew the conclusion that extended
substance is one of the
infiniteattributes of God.
However, in order to
explain more fully, I will refute the arguments of my adversaries, which
all start from the following points:--
[B.] Extended substance, in so
far as it is substance, consists, as they
think, in parts, wherefore they deny that it can be
infinite, or,
consequently, that it can appertain to God. This they illustrate with many
examples, of which I will take one or two.
[1] If extended substance, they
say, is infinite, let it be conceived to be divided into two parts; each
part will then be either finite or infinite. If the former, then infinite
substance is composed of two finite parts, which is absurd. If the latter,
then one infinite will be twice as large as another infinite, which is
also absurd.
[2] Further, if an infinite line be measured out in foot lengths, it will
consist of an infinite number of such parts; it would equally consist of
an infinite number of parts, if each part measured only an inch:
therefore, one infinity would be twelve times as great as the other.
[3] Lastly, if from a single point there be conceived to be drawn two
diverging lines which at first are at a definite distance apart, but are
produced to infinity, it is certain that the distance between the two
lines will be continually increased, until at length it changes from
definite to indefinable. As these absurdities follow, it is said, from
considering quantity as infinite,
the conclusion is drawn, that extended
substance must necessarily be
finite, and,
consequently, cannot appertain to the nature of God.
[C.] The second argument is also drawn
from God's supreme perfection. God,
it is said, inasmuch as he is a supremely perfect being, cannot be
passive;
but extended substance, in so far as it is divisible, is
passive.
It follows, therefore, that extended substance does not appertain to the
essence of God.
[D.] Such are the arguments I
find on the subject in writers, who by them
try to prove that extended substance
is unworthy of the divine nature, and
cannot possibly appertain thereto. However, I think an attentive reader
will see that I have already answered their propositions; for all their
arguments are founded on the hypothesis that extended substance is
composed of parts, and such a hypothesis I have shown (E1P12, and
E1P13C) to be absurd. Moreover, anyone who reflects will see that all
these absurdities (if absurdities they be, which I am not now discussing),
from which it is sought to extract the conclusion that extended substance
is finite, do not at all follow from the notion of an
infinite quantity,
but merely from the notion that an infinite quantity is measurable, and
composed of finite parts: therefore, the only fair conclusion to be drawn
is that
infinite
quantity is not measurable, and cannot be composed of
finite parts. This is exactly what we have already proved (in E1P12).
Wherefore the weapon which they aimed at us has in reality recoiled upon
themselves.
If, from this absurdity of theirs, they persist in drawing the
conclusion that extended substance must be finite, they will in good sooth
be acting like a man who asserts that circles have the properties of
squares, and, finding himself thereby landed in absurdities, proceeds to
deny that circles have any centre, from which all lines drawn to the
circumference are equal. For, taking extended substance, which can only be
conceived as infinite,
one, and indivisible (E1P8,
E1P5, E1P12) they
assert, in order to prove that it is finite, that it is composed of finite
parts, and that it can be multiplied and divided.
So, also, others, after
asserting that a line is composed of points,
can produce many arguments to prove that a line cannot be infinitely
divided. Assuredly it is not less absurd to assert that extended substance
is made up of bodies or parts, than it would be to assert that a solid is
made up of surfaces, a surface of lines, and a line of points.
This must
be admitted by all who know clear reason to be infallible, and most of all
by those who deny the possibility of a vacuum. For if extended substance
could be so divided that its parts were really separate, why should not
one part admit of being destroyed, the others remaining joined together as
before? And why should all be so fitted into one another as to leave no
vacuum? Surely in the case of things, which are really distinct one from
the other, one can exist without the other, and can remain in its original
condition. As, then, there does not exist a vacuum in nature (of which
anon), but all parts are bound to come together to prevent it, it follows
from this also that the parts cannot be really distinguished, and that
extended substance in so far as it is substance cannot be divided.
[E.] If anyone asks me the further question,
Why are we naturally prone to
divide quantity? I answer, that quantity is conceived by us in two ways;
in the abstract
and superficially, as we imagine it; or as
substance, as
we conceive it solely by the
intellect.
If, then, we regard quantity as it is represented in our
imagination,
which we often and more easily do, we
shall find that it is finite, divisible, and compounded of parts; but if
we regard it as it is represented in our
intellect, and conceive it as
substance,
which it is very difficult to do, we shall then, as I have
sufficiently proved, find that it is
infinite, one, and indivisible.
This
will be plain enough to all, who make a distinction between the
intellect
and the
imagination,
especially if it be remembered, that matter is
everywhere the same, that its parts are not distinguishable, except in so
far as we conceive matter as diversely modified, whence its parts are
distinguished, not really, but modally.
For instance, water, in so far as
it is water, we conceive to be divided, and its parts to be separated one
from the other; but not in so far as it is extended
substance; from this
point of view it is neither separated nor divisible. Further, water, in so
far as it is water, is produced and corrupted; but, in so far as it is
substance, it is neither produced nor corrupted.
[F.] I think I have now answered the
second argument; it is, in fact,
founded on the same assumption as the first-- namely, that matter, in so
far as it is substance, is divisible, and composed of parts. Even if it
were so, I do not know why it should be considered unworthy of the divine
nature, inasmuch as besides God (by E1P14) no
substance can be granted,
wherefrom it could receive its modifications. All things, I repeat, are in
God, and all things which come to pass, come to pass solely through the
laws of the
infinite
nature of God, and follow (as I will shortly show)
from the necessity of his essence. Wherefore it can in nowise be said,
that God is passive
in respect to anything other than himself, or that
extended substance is unworthy of the Divine nature, even if it be
supposed divisible, so long as it is granted to be infinite and eternal.
But enough of this for the present.

E1:
PROP. 16. From the necessity of the divine nature must follow an
infinite number
of things in infinite
ways--that is, all things which can fall within the sphere of
infiniteintellect.

Proof.--This proposition will
be clear to everyone, who remembers that
from the given definition
of any thing the
intellect infers several
properties, which really necessarily follow therefrom (that is, from the
actual essence
of the thing defined); and it infers more properties in
proportion as the definition of the thing expresses more reality, that is,
in proportion as the essence
of the thing defined involves more reality.
Now, as the divine nature has absolutely
infiniteattributes (by
E1D6), of which each expresses
infinite essence
after its kind, it
follows that from the necessity of its nature an
infinite number of things
(that is, everything which can fall within the sphere of an
infiniteintellect)
must necessarily follow. Q.E.D.

Proof.--We have just shown
(in E1P16), that solely from the necessity
of the divine nature, or, what is the same thing, solely from the
laws of his nature, an
infinite
number of things absolutely follow in an infinite
number of ways; and we proved (in E1P15), that without God nothing can
be nor be conceived; but that all things are in God. Wherefore nothing can
exist outside himself, whereby he can be conditioned or constrained to act.
Wherefore God acts solely by the
laws of his own nature, and is not
constrained by anyone. Q.E.D.

E1: PROP. 17, Note.
--[A.] Others think that God is a free cause, because he can, as they think,
bring it about, that those things which we have said follow from his
nature--that is, which are in his power, should not come to pass, or
should not be produced by him. But this is the same as if they said, that
God could bring it about, that it should follow from the nature of a
triangle, that its three interior angles should not be equal to two right
angles; or that from a given cause no effect should follow, which is
absurd.
Moreover, I will show below,
without the aid of this proposition, that
neither intellect
nor will appertain to God's nature. I know that there
are many who think that they can show, that supreme intellect and
free will
do appertain to God's nature; for they say they know of nothing more
perfect, which they can attribute to God, than that which is the highest
perfection in ourselves.
Further, although they conceive God as actually
supremely intelligent, they yet do not believe, that he can bring into
existence everything which he actually understands, for they think that
they would thus destroy God's power. If, they contend, God had created
everything which is in his intellect, he would not be able to create
anything more, and this, they think, would clash with God's omnipotence;
therefore, they prefer to assert that God is indifferent to all things,
and that he creates nothing except that which he has decided, by some
absolute exercise of will, to create.
However, I think I have shown
sufficiently clearly (by E1P16), that from God's supreme power, or
infinite
nature, an infinite number of things--that is, all things have
necessarily flowed forth in an infinite number of ways, or always follow
from the same necessity; in the same way as from the nature of a triangle
it follows from eternity and for eternity, that its three interior angles
are equal to two right angles. Wherefore the omnipotence of God has been
displayed from all eternity, and will for all eternity remain in the same
state of activity.
This manner of treating the question attributes to God
an omnipotence, in my opinion, far more perfect.
For, otherwise, we are
compelled to confess that God understands an infinite number of creatable
things, which he will never be able to create, for, if he created all that
he understands, he would, according to this showing, exhaust his
omnipotence, and render himself imperfect. Wherefore, in order to
establish that God is perfect, we should be reduced to establishing at the
same time, that he cannot bring to pass everything over which his power
extends; this seems to be a hypothesis most absurd, and most repugnant to
God's omnipotence.
[B.]Further
(to say a word here concerning the
intellect and the
will which
we attribute to God), if intellect and will appertain to the eternal
essence of God, we must take these
words in some significations quite
different from those they usually bear. For intellect and will, which
should constitute the essence of God, would perforce be as far apart as
the poles from the human intellect and will, in fact, would have nothing
in common with them but the name; there would be about as much
correspondence between the two as there is between the Dog, the heavenly
constellation, and a dog, an animal that barks. This I will prove as
follows.
If intellect belongs to the divine
nature, it cannot be in
nature, as ours is generally thought to be, posterior to, or simultaneous
with the things understood, inasmuch as God is prior to all things by
reason of his causality (E1P16C1). On the contrary,
the truth and
formal essence
of things is as it is, because it exists by
representation as such
in the intellect of God.
Wherefore the intellect of God, in so far as it
is conceived to constitute God's
essence, is, in reality, the cause of
things, both of their essence and of their existence. This seems to have
been recognized by those who have asserted, that God's
intellect, God's
will,
and God's power, are one and the same. As, therefore, God's
intellect
is the sole cause of things, namely, both of their
essence and
existence, it must necessarily differ from them in respect to its essence,
and in respect to its existence. For a cause differs from a thing it
causes, precisely in the quality which the latter gains from the former.
For example, a man is the cause of another man's existence, but not of
his essence (for the latter is an
eternal truth),
and, therefore, the two
men may be entirely similar in essence, but must be different in
existence; and hence if the existence of one of them cease, the existence
of the other will not necessarily cease also; but if the
essence of one
could be destroyed, and be made false, the essence of the other would be
destroyed also.
Wherefore, a thing which is the
cause both of the essence
and of the existence of a given effect, must differ from such effect both
in respect to its essence, and also in respect to its existence. Now the
intellect of God is
the cause of both the essence
and the existence of our
intellect;
therefore, the intellect of God in so far as it is conceived to
constitute the divine essence, differs from our intellect both in respect
to essence and in respect to existence, nor can it in anywise agree
therewith save in name, as we said before. The reasoning would be
identical in the case of the
will, as anyone can easily see.

E1:
PROP. 18. God is the indwelling [immanens] and not the transient cause of all
things.

Proof.--All things which are,
are in God, and must be conceived through
God (by E1P15), therefore
(by E1P16C1) God is the cause of those
things which are in him. This is our first point. Further, besides God
there can be no substance
(by E1P14),
that is [E1D3] nothing in itself external
to God. This is our second point. God, therefore, is the indwelling and
not the transient cause of all things. Q.E.D.

Proof.--God
(by E1D6) is
substance, which
(by E1P11) necessarily
exists, that is (by E1P7) existence
appertains to its nature, or (what
is the same thing) follows from its
definition; therefore, God is
eternal
(by E1D8). Further, by the
attributes of
God we must understand that
which (by E1D4) expresses the
essence of
the divine substance --in
other words, that which appertains to substance: that, I say, should be
involved in the attributes
of substance. Now
eternity appertains to the
nature of substance (as I have already shown in
E1P7); therefore,
eternity must appertain to each of the
attributes, and thus all are
eternal. Q.E.D.

E1: PROP. 19, Note.
--This proposition is also evident from the manner in which (in
E1P11) I demonstrated the
existence of God;
it is evident, I repeat,
from that proof, that the
existence of God,
like his essence, is an
eternal truth.
Further (in Prop. 19. of my " Principles of the Cartesian
Philosophy"), I have proved the eternity of God, in another manner, which
I need not here repeat.

Proof.--God
(by the last Prop E1P19) and all his
attributes are
eternal,
that is (by E1D8) each
of his attributes expresses existence.
Therefore the same attributes
of God which [E1D4] explain his
eternalessence,
explain at the same time his
eternal existence --in other words, that which
constitutes God's essence constitutes at the same time his existence.
Wherefore God's existence
and God's essence
are one and the same. Q.E.D.